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ValentinkaMS [17]

2 years ago

12

A family installs and fills an aboveground pool. The swimming pool costs $850 to install, and it costs $75 per thousand gallons

of water to fill.
Which function represents the total cost, C, of installing and filling a pool with x thousands of gallons of water?

1 answer:

kari74 [83]2 years ago

6 0

Answer:

925????

Step-by-step explanation:

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Find the value of k that makes f(x) continuous at x = -1

lozanna [386]

Answer:

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Step-by-step explanation:

3 0

2 years ago

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Nia has number cards 2,3,8,9, and 5 . What are the different way bus can arrange the cards to show only even numbers with 2 in t

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8 0

3 years ago

PLZ HELP!!! Use limits to evaluate the integral.

Marrrta [24]

Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:

$\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]$

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

$r_i=\dfrac{2i}n$

where $1\le i\le n$ . Each interval has length $\Delta x_i=\frac{2-0}n=\frac2n$ .

At these sampling points, the function takes on values of

$f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}$

We approximate the integral with the Riemann sum:

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3$

Recall that

$\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4$

so that the sum reduces to

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}$

Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:

$\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}$

Just to check:

$\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28$

4 0

2 years ago

Please help version 2

Juli2301 [7.4K]

Answer:

16°

Step-by-step explanation:

2x° + 6° = 38°

x° = (38°- 6°)÷2=16°

3 0

2 years ago

I am so confused! Can anyone help me with this trig problem?

Dominik [7]

$\frac{5\pi }{4}$ or $\frac{7\pi }{4}$

divide both sides by 2

sinΘ = - $\frac{\sqrt{2} }{2}$

Since the sin ratio is negative then Θ is in third / fourth quadrants

Θ = $sin^{- 1}$ ( $\frac{\sqrt{2} }{2}$ ) = $\frac{\pi }{4}$ related acute angle

Θ = ( π + $\frac{\pi }{4}$ ) = $\frac{5\pi }{4}$

or Θ = ( 2π - $\frac{\pi }{4}$ ) = $\frac{7\pi }{4}$

4 0

2 years ago